**"Area"**

## Years 9 – 12 Differences of Squares Investigation

*By toni On 15 November, 2019 · Leave a Comment*

1. What do you see in this picture?

Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .

2. What do you notice about the difference between squares of consecutive numbers?

Compare the differences between squares of numbers that differ by 1 […]

## Years 10 – 12 Quadratic Equations

*By Kwethemba Moyo On 14 September, 2019 · Leave a Comment*

John plans to get the minimum possible Diamond Razor Mesh fencing material, as a security measure to discourage entry into his dam. He finds out that the rectangular shape drawn around the dam picture can help. The dimensions are given in algebraic form, in metres. Find an expression for the area of this […]

## Years 6 – 8 Can you help these Farmers?

*By Elizabeth Turok On 5 September, 2019 · Leave a Comment*

A large piece of land, divided into small plots, belongs to 5 different farmers.

Below is a plan of the area as the land is presently divided.

All the plots labelled (a) belong to farmer (a).

All the plots labelled (s) belong to farmer (s) and so on.

## Years 7 – 10 ALGEBRAREA Product of two brackets and area

*By Kwethemba Moyo On 15 August, 2019 · Leave a Comment*

1. You have 2 blue shapes, 3 green and 5 brown. Describe their properties.

2. Find the areas in square units of the 3 pieces blue, green and brown.

3. Build one big geometrical shape using all 10 pieces, placing them edge to edge. Draw […]

## Years 4 – 7 Two by Two Puzzle

*By toni On 25 August, 2018 · Leave a Comment*

Can you find numbers to replace the ? marks to solve this two by two multiplication puzzle? Can you explain how it works?

How does the diagram below connect with the multiplication?

Use the two grids to do the two multiplications:

72 × 25 […]

## Years 11 – 12 Solve the triangle

*By toni On 18 August, 2018 · Leave a Comment*

The area of triangle PQR is 3√3 square centimetres. Angle PRQ is 60 degrees and RQ is 4 centimetres longer than PR.

Find the length of PQ.

Draw ΔPQR accurately.

Calculate all the angles in the triangle.

## Grades 5 to 8 Wholesome Rectangles

*By toni On 15 October, 2017 · Leave a Comment*

This activity is about rectangles with whole number dimensions. With other lengths and breadths there are infinitely many possible rectangles so here we just stick to whole numbers.

How many rectangles can you make with perimeter 12 units?

What do you know about rectangles? What is the smallest rectangle that you can […]

## Years 9 to 11 Kissing Triangles

*By toni On 19 July, 2017 · Leave a Comment*

Find the total area of the two triangles by two different methods if ACD and BCE are straight lines .

What are the lengths PC and CQ?

The triangles are re-drawn keeping the total area the same and keeping the distances between the green parallel lines as 3 cm and BD = 4 cm.

## Years 8 – 10 GRAPHICAL TRIANGLE

*By toni On 16 November, 2016 · Leave a Comment*

What is the area, (in square units) of the triangle formed by the three lines whose equations are: y − x = 6, x − 2y = 3 and x + y = 6?

Lick here to download the GRAPHICAL TRIANGLE worksheet

Click here for the Notes for Teachers.

This […]

## Grades 7 to 10 Painted Cube

*By toni On 5 November, 2016 · 22 Comments*

Imagine a large cube made up from 27 small red cubes each measuring 1 cm by 1 cm by 1 cm. What is its volume?

Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered. What is its surface area?

Now imagine breaking the […]

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